Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The England Under-21 international went straight into the North End squad for their League One trip to Crawley on Tuesday night, but the game was later postponed due to a waterlogged pitch.
Rudd has played three cup games for the Canaries this season, including the shock weekend FA Cup defeat to non-league Luton.
Earlier this month, North End cancelled the contract of goalkeeper Steve Simonsen by mutual consent.